It means I don't have a romantic partner (boyfriend or girlfriend or spouse).

revised tks!!! I totally understand now

tks!!! I am totally understand now.

a "duo" is two people, a "trio" is three people, and "solo" is just one person, like when the singer from a band starts to make music by themself it's called a "solo project" or "solo act". so like the guy above me said, in the context of a song about love it would mean not having a girlfriend or boyfriend. makes you think of someone riding around by themself in a car or the "lone cowboy" character from movies that rides around on a horse in the desert by himself.